"Fond regards" implies that you know the person well, and like them very much. It is not appropriate for formal letters. In England, we might say "she is very fond of horses"; we actually mean she adores horses!
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My Father a few months before he passed away sent what would be His last birthday card to me.
He signed the card off:
'With Fondest Regards'
I thought this strange as wondered why he didn't say love. For a while I found it difficult to reconcile as was a little hurt. After he passed on I confided in a friend and they reframed this for me. Often we sign a card off 'with love'